110 Ratio of the Length and Height of Bea Waves. 



been attracted during a few years past, is at present in an 

 immature or rather embryonic state, as indeed is continually 

 pointed out by its most eminent followers. The views and 

 suggestions of any observer, however humble, are of value ; 

 and the store of information which the British and French 

 Admiralties — ever rivals in scientific progress — are now en- 

 gaged in collecting, through their naval officers, in all parts 

 of the world, must soon tend to formulate a completed theory 

 of the subject. The extraordinary length of some waves 

 in comparison with their height has often attracted the 

 notice and the vague surprise of observers long even before 

 the attention of mathematicians was drawn into the in- 

 quiry. In a recent Admiralty circular Mr. Froude 

 cautions officers observing waves that they must not 

 neglect those of almost imperceptible height but from 

 600 to 1000 feet in length, which greatly influence the roll- 

 ing movement of a ship. On the southern coast of Aus- 

 tralia there is a well-known and remarkable difierence in 

 this respect in the character of the swell from the eastward 

 and the westward. The south-east and the south-west direc- 

 tions there extend over equally great stretches of ocean, but 

 while the swell from the south-east is a short chopping sea, 

 high and steep (usually 8 or 9 feet high and 150 feet long, 

 or as 1 to 17), that from the westward is a long heavy roll, 

 usually about the same height (8 or 9 feet) but 150 yards 

 instead of feet in length, or as 1 : 151. What I would here 

 attempt to show, or rather to suggest, is that the varying 

 ratio of height to length signifies or rather represents none 

 other than the process of increase or subsidence of waves, 

 and that if we could follow a sea- wave from its genesis to 

 actual extinction we should be able to observe it through 

 all the various phases as to height and length which have 

 been enumerated. 



That a certain force of wind acting for a given time will 

 produce a wave of definite form is, I suppose, undoubted ; 

 and I presume it will not be questioned that the same con- 

 ditions will always produce the precisely similar wave whose 

 height is in a given ratio to its length. A certain force of 

 wind, again, sufficient to obviate the loss by friction, will 

 sustain in it this form ; but if the sustaining force be with- 

 drawn, then, however far its momentum will carry it — and 

 it is known to carry it thousands of miles — the wave must 

 thence gradually decline ; and it is in this decline, viz., from 



